Numerical study of a microscopic artificial swimmer

Gauger, Erik M.; Stark, Holger

doi:10.1103/physreve.74.021907

Cited by 168 publications

(204 citation statements)

References 37 publications

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“…Related studies include the dynamics of magnetic filaments [23][24][25], the three-dimensional actuation and instabilities of flexible filaments [26][27][28][29] and the exploitation of symmetry-breaking to pump fluid in a channel [30].…”

Section: Introductionmentioning

confidence: 99%

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Floppy swimming: Viscous locomotion of actuated elastica

2007

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Actuating periodically an elastic filament in a viscous liquid generally breaks the constraints of Purcell's scallop theorem, resulting in the generation of a net propulsive force. This observation suggests a method to design simple swimming devices -which we call "elastic swimmers" -where the actuation mechanism is embedded in a solid body and the resulting swimmer is free to move. In this paper, we study theoretically the kinematics of elastic swimming. After discussing the basic physical picture of the phenomenon and the expected scaling relationships, we derive analytically the elastic swimming velocities in the limit of small actuation amplitude. The emphasis is on the coupling between the two unknowns of the problems -namely the shape of the elastic filament and the swimming kinematics -which have to be solved simultaneously. We then compute the performance of the resulting swimming device, and its dependance on geometry. The optimal actuation frequency and body shapes are derived and a discussion of filament shapes and internal torques is presented. Swimming using multiple elastic filaments is discussed, and simple strategies are presented which result in straight swimming trajectories. Finally, we compare the performance of elastic swimming with that of swimming microorganisms. I. INTRODUCTIONThe fluid mechanics of microorganism locomotion, pioneered more than fifty years ago by G.I. Taylor, has become one of the most successful branches of biomechanics, with success in both the basic physical understanding of flow behavior and the quantitative prediction of kinematics and energetics of locomotion [1][2][3][4][5][6][7][8].Recent technical advances have led to ever more precise fabrication at small scales (microns or less), prompting both theorists [9-13] and experimentalists [14] to design and analyze a series of simple low-Reynolds number swimmers. The experiment of Dreyfus et al. [14], in particular, reported locomotion in a sperm-like micro-swimmer, composed of a cargo (red blood cell) and a slender flexible filament made of a series of paramagnetic beads. In that case, actuation by oscillating transverse magnetic fields led to the generation of bending waves propagating along the filament and resulted in the motion of the micro-swimmer. In this system, the right-left symmetry was broken by the presence of a cargo and led to a preferential tip-to-base propagation of the bending waves, resulting in locomotion in the direction base-to-tip.An alternative way to break the symmetry in a similar system would be to build-in the asymmetry in the actuation. In particular, if an elastic filament is periodically actuated at one of its extremities in a viscous liquid, the resulting motion will lead to the propagation of bending waves and, in general, propulsive forces. This idea was originally proposed by Edward Purcell [8]. Physically, actuating an elastic filament allows one to break the constraints of the "scallop theorem" -which states that a body performing a reciprocal motion at low Reynolds number cannot p...

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Section: Introductionmentioning

confidence: 99%

“…Related studies include the dynamics of magnetic filaments [23][24][25], the three-dimensional actuation and *…”

Section: Introductionmentioning

confidence: 99%

Floppy swimming: Viscous locomotion of actuated elastica

2007

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“…Here κ b is the bending stiffness and θ is the angle between two bond vectors that point from one vertex to its two nearest neighbors [13].…”

Section: Taylor Sheetmentioning

confidence: 99%

Swimming at Low Reynolds Number: From Sheets to the African Trypanosome

Babu

Schmeltzer

Stark

2012

Notes on Numerical Fluid Mechanics and Multidisciplinary Design

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Abstract. The African trypanosome is a protozoan which causes sleeping sickness in mammals. To study the dynamics of this microorganism at low Reynolds number, we implement and investigate three swimmer models, the Taylor sheet, a constanttorque swimmer, and a model for the African trypanosome. The first two swimmers are based on a semi-flexible sheet and the third is a full three-dimensional model. We simulate the viscous fluid environment of the swimmers using a technique called multi-particle collision dynamics. We verify our technique by implementing the Taylor sheet which is activated by a bending wave traveling along the sheet. Its ballistic motion turns into diffusive motion when the sheet becomes passive. For the constant-torque swimmer we apply a torque to the semi-flexible sheet which assumes a cork-screw shape and then generates the thrust force for propelling the swimmer forward. Whereas the angular velocity scales linearly with the torque, the swimming velocity displays a non-linear dependence. Finally, our trypanosome model swims with the help of a beating flagellum attached to the cell body. Since it wraps around the body, the model trypanosome displays a helical swimming trajectory. The swimming velocity displays a non-linear increase with the beating frequency of the flagellum.

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“…Also, since the pioneering theoretical works of Jeffery (1922) on the dynamics of ellipsoidal particles, the study of fibres in Newtonian fluid flows has been the subject of many experimental and numerical studies, with motivations as diverse as papermaking, water 40 purification, dynamics of DNA molecules or microswimmers (Forgacs and Mason, 1959;Yamamoto and Matsuoka, 1996;Ross and Klingenberg, 1997;Switzer and Klingenberg, 2003;Subramanian and Koch, 2005;Gauger and Stark, 2006;Lindström and Uesaka, 2007;Wandersman et al, 2010;Lindner and Shelley, 2015;Farutin et al, 2016). In particular, fibre suspensions have often been mod-45 elled by studying the interactions between a laminar simple shear or Poiseuille flow and flexible rods modelled as strings of spherical (or circular) beads.…”

Section: Introductionmentioning

confidence: 99%

“…Discretizing the bending free energy of a continuous elastic rod gives the following expression for the bending force acting on the particle i 5 (Gauger and Stark, 2006;S lowicka et al, 2012):…”

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confidence: 99%

Dynamics of a flexible fibre in a sheared two-dimensional foam: Numerical simulations

Langlois

Hutzler

2017

Colloids and Surfaces A: Physicochemical and Engineering Aspect

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Recently there has been a renewed interest in using foamy suspensions of wood fibres as a carrier fluid in papermaking but there is a lack of fundamental understanding of the dynamics of such a three-phase system. In this article we propose a numerical model for the dynamics of an individual flexible fibre within a flowing foam, based on discrete-element methods. As is observed in a Newtonian shear flow, we observe that the fibre systematically experiences a tumbling instability: the disordered motion of bubbles cannot prevent the pseudo-periodical flip of the fibre. Our simulations show that the tumbling time decreases almost as the inverse of the strain rate. It also decays when the fibre length is increased, though for long enough fibres it reaches a constant value. Similarly the tumbling time is also surprisingly independent of the stiffness of the fibre. Because of their tumbling motion, long and flexible fibres spend most of the time in a coiled geometry. This would imply that using foam as a carrier fluid is not enough to keep fibres aligned with the flow. However, further refinements of the model will need to be considered to arrive at firm conclusions regarding alignment. Dear Editor,We would like to thank the referee for his careful reading and constructive remarks. We tried to follow his recommendations, and to answer his comments and concerns regarding the article. The modifications we brought to the paper are listed below:Reviewer #1 * General questions that seem not to be addressed are: Is there shear-banding or localisation? Does it matter where between the side walls the fibre is placed? (I guess it shouldn't, but I presume that this was checked.)Since no additional wall friction is added (see our previous study of the bubble model in Langlois et al. [2008]), no shear-banding is observed. The average velocity profile is mostly undisturbed by the presence of a unique fibre, and remains linear.The initial y-position of the fibre is of no influence, except in the 'pathological' case where it comes in contact with one of the walls and remains there.* lines 10-20 are not very clear on how the presence of the fibres affects these foam properties; it would be useful to expand this section to give the reader more of a feel for the complexity of this area of research and the way in which a foam interacts with fibres.We have added to the introduction a more thorough description on the effects of fibres on the foam, recently observed experimentally (l.15 to 21).* lines 63 and 96: I find the use of the word "spherical" misleading, since in a 2D experiment bubbles are more discoidal than spherical and they are certainly treated here as discs. Once the description of the bubble model is restricted to 2D, I suggest to use "discs" exclusively.In the simulations the bubbles are indeed treated as disks, though we had initially used the term "spheres" since these disks are meant to mimick a bubble raft made of roughly spherical bubbles seen from above. However we agree that this can lead to some confusion...

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Numerical study of a microscopic artificial swimmer

Cited by 168 publications

References 37 publications

Floppy swimming: Viscous locomotion of actuated elastica

Floppy swimming: Viscous locomotion of actuated elastica

Swimming at Low Reynolds Number: From Sheets to the African Trypanosome

Dynamics of a flexible fibre in a sheared two-dimensional foam: Numerical simulations

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